Linear Matrix Inequality Conditions and Duality for a Class of Robust Multiobjective Convex Polynomial Programs

DOI10.1137/17M1143484zbMath1406.90111MaRDI QIDQ5376453

Thai Doan Chuong

Publication date: 18 September 2018

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

zbMATH Keywords

linear matrix inequalitydualitymultiobjective optimizationrobust optimizationSOS-convex polynomial

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Numerical optimization and variational techniques (65K10) Optimality conditions and duality in mathematical programming (90C46)

Related Items (18)

Optimality and duality in nonsmooth composite vector optimization and applications ⋮ Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data ⋮ Robustness in nonsmooth nonconvex optimization problems ⋮ Second-order cone programming relaxations for a class of multiobjective convex polynomial problems ⋮ Conic linear programming duals for classes of quadratic semi-infinite programs with applications ⋮ Optimality conditions for robust weak sharp efficient solutions of nonsmooth uncertain multiobjective optimization problems ⋮ Characterizing robust optimal solution sets for nonconvex uncertain semi-infinite programming problems involving tangential subdifferentials ⋮ Robust duality for nonconvex uncertain vector optimization via a general scalarization ⋮ A utopia point method-based robust vector polynomial optimization scheme ⋮ Characterizing a class of robust vector polynomial optimization via sum of squares conditions ⋮ Robust Optimality and Duality in Multiobjective Optimization Problems under Data Uncertainty ⋮ On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems ⋮ Robust second order cone conditions and duality for multiobjective problems under uncertainty data ⋮ A hybrid approach for finding efficient solutions in vector optimization with SOS-convex polynomials ⋮ Optimality and duality in nonsmooth conic vector optimization ⋮ Exact relaxations for parametric robust linear optimization problems ⋮ Unified robust necessary optimality conditions for nonconvex nonsmooth uncertain multiobjective optimization ⋮ Robust Pareto solutions for convex quadratic multiobjective optimization problems under data uncertainty

Uses Software

• CVX
• ParetoImageSDP

Cites Work

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• WHAT IS...a Spectrahedron?
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• Semidefinite Optimization and Convex Algebraic Geometry
• Multicriteria Optimization
• Convex Analysis
• Optimality and duality for robust multiobjective optimization problems
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